Simplify cot(pi/2-a)cos(a)

Problem

cot(π/2−a)*cos(a)

Solution

1. Apply the cofunction identity for the cotangent function, which states that cot(π/2−θ)=tan(θ)

cot(π/2−a)=tan(a)

2. Substitute the identity back into the original expression.

tan(a)*cos(a)

3. Rewrite the tangent function using the quotient identity tan(a)=sin(a)/cos(a)

sin(a)/cos(a)⋅cos(a)

4. Simplify the expression by canceling the common factor of cos(a) in the numerator and denominator.

sin(a)

Final Answer

cot(π/2−a)*cos(a)=sin(a)

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